The Cut-and-Play Algorithm: Computing Nash Equilibria via Outer Approximations

When players in a game face messy decisions—like yes/no choices, rules layered within rules, or conflicting objectives—traditional algorithms often fail to find stable outcomes. Carvalho, Dragotto, Lodi, and Sankaranarayanan introduce a new algorithm, Cut-and-Play, that breaks this barrier. Unlike previous methods, Cut-and-Play handles nonconvex and unbounded decision spaces—the kind often found in real-world markets, public policy, and artificial intelligence systems. It works by iteratively solving simpler approximations of a complex game and then refining them with mathematical “cuts” until a solution is reached. Most strikingly, the algorithm finds equilibria up to 10× faster than existing techniques and is the first of its kind to offer a general-purpose solution method for this class of problems. The work is a leap forward for both the theory and application of strategic decision making.